Method for detecting geometrical-optical aberrations

ABSTRACT

The invention relates to a method for determining geometrical-optical aberrations up to and including 3rd order in particle-optical, probe-forming systems, in particular scanning electron microscopes, comprising an essentially punctiform source, lenses, an object, and a detector, the image being recorded, the process being repeated with an overfocussed and an underfocussed beam, the images being transformed in Fourier space, the transformation of the overfocussed image, and the underfocussed image is divided by the transformed focussed image. The results are reverse transformed, and the brightness profiles of the probes, the images of the source, are determined in overfocus and underfocus. The asymmetry, the width and/or the curvature of the profile being determined in the center, and the image aberration being determined from the differences.

This application is the national phase under 35 U.S.C. §. 371 of PCTInternational Application No. PCT/DE00/04578 which has an Internationalfiling date of Dec. 20, 2000, which designated the United States ofAmerica.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a method for determininggeometrical-optical aberrations up to and including 3rd order inparticle-optical, probe-forming systems, in particular scanning electronmicroscopes comprising an essentially punctiform source, which emits theparticles, lenses for influencing the particle beam, an object, which isimaged by the particles, and a detector for registering the particles orimaging the object, the object being imaged by a particle beam focussedon the object, and the image being recorded; the process being repeatedwith an overfocussed and an underfocussed beam, which produce the images(overfocussed) and (underfocussed), the images being transformed inFourier space, the transformation of the overfocussed image beingdivided by that of the transformed focussed image, and the quotientbeing obtained, and the transformation of the underfocussed image beingdivided by that of the transformed focussed image and the quotient beingobtained.

2. Description of the Background Art

Scanning electron microscopes operate according to the principle that asharply focussed electron beam, whose diameter determines the efficiencyand resolution, is guided line by line over an object surface to beanalyzed. The electrons passing through the object or scattered backtherefrom, or the secondary electrons released in the object surface,are either collected in a collector or amplified by means of ascintillator and a downstream photomultiplier and used for controllingthe display. For emission of the electrons, a source under high voltageis used, which usually takes the form of a tungsten tip, whose diameteris of the order of a few nm. Via the tip, an essentially punctiformparticle source can be provided with virtually any accuracy. The imageof the source, that is to say the tungsten tip, of the microscope opticsis usually described as the probe.

In the case of particle optical systems, in particular scanning electronmicroscopes, the resolution capacity and the quality of the image islimited, inter alia, by the geometrical-optical aberrations, which havethe consequence that punctiform objects are not reproduced in an ideallypunctiform manner in the image. In the vicinity of the theoretical imagepoint, the caustic is produced as the envelope of the rays actuallyintersecting in its vicinity. Spherical aberration is known, in whichthe axially parallel incident rays intersect in the image spacerespectively before or after the image point supplied by the paraxialrays. The axial image aberrations of higher “foldedness” lead toenlargements of the image point, which will be different depending onthe azimuth. In the case of two-fold astigmatism, a circular object inthe image plane is distorted into an elliptical image, since themeriodonal and sagittal rays perpendicular thereto have different focallengths. For correction of these axial imaging aberrations extending upto a 3rd order, it is known to use correctives consisting ofnon-circular lens systems, as well as, for example from PCT/DE98/02596,a method for eliminating all axial image aberrations up to the 3rdorder, in order to increase the resolution capacity.

The article in Japanese Journal Appl. Phys., Volume 38 (1999), pages957ff, and GB 2 305 324 A disclose methods for determining 1st orderimage aberrations, in which the images from two different focussings aretransformed in Fourier space and, by forming the quotient, are used fordetermining the image aberration coefficients. The method describedhere, however, is unsuitable for determining higher order imageaberrations.

A disadvantage of this can be seen in the fact that the informationobtained in the image point is determined both by the optical imageaberrations of the imaging, probe-forming optical system and by theobject structure itself. For determination of the image aberration, itwould therefore be necessary to know the object structure, in order,from the image obtained, and the known object structure to be able todraw conclusions about the nature and size of the image aberration.

SUMMARY OF THE INVENTION

It is therefore an object of the present invention to provide a method,with which the geometrical-optical imaging aberration can be determined,without an exact knowledge of the object structure, which is imaged bythe particle beam emitted by the source.

According to the invention, this object is achieved in that bothquotients are reverse transformed and thereby the brightness profiles ofthe probes, that is to say of the images of the source in overfocus andunderfocus, are determined. The asymmetry of the profiles with respectto the center, the width of the profiles, in particular the half-valuewidth, and/or the curvature of the profiles in the center aredetermined, and the differences of the profiles of the probes withrespect to these parameters are used to determine the image aberrations.

The basic finding of the invention is in the fact that, ontransformation of the images of the object with a particle beam focussedon the object and an overfocussed and an underfocussed particle beam,and by subsequent division of the transforms in Fourier space, theobject structure is cancelled out of the obtained quotients. The imagecorresponds mathematically to a folding of the object with a focussed ordefocussed probe, that is to say in Fourier space to a product of objectinformation and probe information. Consequently, after the Fouriertransformation, the object information can be cancelled out by adivision of the two transforms. That means that, by division in Fourierspace, the information, contained in the transformations of the images,about the object to be imaged can be eliminated, so that the informationabout the optical image aberrations remains. In conventionalterminology, the terms underfocussed and overfocussed mean that theparticle beam is not focussed in the object plane, but before or afterit with respect to the optical axis. If the defocus is large withrespect to the probe diameter, with an image with a focussed particlebeam, the focussed image is an approximately adequate reproduction ofthe object structure. The condition necessary for this, of anessentially punctiform source, is sufficiently satisfied by theabove-described tungsten tip. In this case the defocussed probe, that isto say an image of the source with a defocussed particle beam, can beobtained from the reverse transformation of the quotient, which nolonger contains information about the object structure. After thisreverse transformation, the geometrical-optical image aberrations aredetermined, which lead to the distortion of the probe profiles. To thisend, sections are formed through the probe profiles to determine theprofiles of intensity, or brightness, of the images in the profile, thatis to say perpendicular to the optical axis. The sections are, asdiscussed below, formed at equidistant angular intervals, in order alsoto determine the brightness and intensity distribution of the Imageabout the optical axis. To determine the geometrical-optical imageaberrations, the asymmetry of the profiles with respect to the centerare determined by subtracting the measurement values of the sections tothe left and right of the center from one another, the width of thesection, the half-value width and/or its curvature in the center usuallybeing chosen here to simplify the evaluation. From these values, whichare usually different, for the overfocussed and underfocussed probes,mean values and/or differences can also be formed. These angle-dependentvalues can be used to determine the image aberrations, and from thelatter, by setting a corrective or by a mathematical imagereconstruction methods, the correction can be made to obtain a sharp,undistorted image.

The advantage of the invention is in the fact that only one object needsto be imaged multiply in order, from the focussed, overfocussed andunderfocussed images, to determine the geometrical-imaging aberrationwithout the actual structure of the object needing to be known. Fromthis, correction parameters can be determined, with which, withsubsequent measurement series and different objects, the obtainedmeasurement results, i.e. images, can be corrected to obtain a sharpimage. To this end the optics of the system are analogously adjusted byappropriately setting a corrective, or mathematical correction methodsare applied, to compensate for the aberrations.

For carrying out the Fourier transformation in the case of a particlebeam focussed or defocused on the object, it is proposed that thetransformation be carried out mathematically, in particular according tothe fast-Fourier transformation known to one skilled in the art. Inprinciple, it is also possible to carry out such a transformation in ananalogous manner by producing a diffraction pattern. With the samemethod, reverse transformations of the respective quotients can also becarried out.

In particular in the case of scanning electron microscopes, the lensesfor influencing the direction of the electron beam have electricaland/or magnetic multipoles, since these can focus and deflect theelectron beam in a known manner. With these types of lenses, acorrection of the geometrical-optical imaging aberration can also beprovided in a simple manner, since a correction factor determined by themethod described above, can be applied to the electrical and/or magneticfields, that is to say they can be varied, to obtain an aberration-freeimage of the object.

To ensure that the information about the object structure is actuallycancelled out by division in Fourier space, the width of the focussedprobe, that is to say the image of the source in the defocussed state,must be at least ten times greater than the width of the focussed probe,or the actual width of the particle source.

Advantageously, the sections through the probe profiles are placed atequidistant angular intervals, in particular every 15 degrees, to obtainadequate resolution of the brightness or intensity profiles about theoptical axis. To determine the geometrically optical imagingaberrations, the “foldednesses” of the sections are analyzed, that is tosay how many planes of symmetry the probe profile has perpendicular tothe optical axis.

The asymmetry of the sections serve for determining the second orderimage aberration. Since these ought to be theoretically the same inoverfocus and underfocus, the mean value can be formed from the twomeasurements for further analysis. This mean value formed from overfocusand underfocus and depending on the section angle w, is subjected toanalysis, with respect to the section angle of the one-fold andthree-fold angle components, for example by a Fourier analysis,according to the section angle w. The one-fold component, regarding theorientation and magnitude, represents the value of the 2nd order axialcoma. The three-fold component of the analysis supplies, regardingorientation and magnitude, the value of the three-fold 2nd orderastigmatism.

The widths and curvatures of the probe profiles, which are dependent onthe section angle w, can be used for the determination of furthergeometrical-optical image aberrations. In general terms, the width BR ofthe probe profiles provides a basis for determining the 1st order imageaberration, and the determined values of curvature for determining thevalues of the 3rd order image aberration. For analysis, however, thefollowing procedure is necessary: the common feature is that thedifferences between the measured values for overfocus and underfocus aredetermined in dependence on the section angle w. In the aberration-freecase, the differences would disappear. Here, too, an analysis of theobtained difference values according to their foldedness with respect tothe section angle w should be carried out, for example by the Fourieranalysis. In this way, the spectrum components, ordered according totheir foldedness, are obtained in dependence on the section angle w. Thecorresponding foldedness permits the assignment to the correspondinggeometrical-optical image aberrations, the quantitative value, and,apart from the rotationally symmetrical image aberrations, itsorientation provide information about the magnitude and, possibly, thealignment of a particular image aberration. In principle, the widths ofthe probe profiles and/or the differences in overfocus/underfocus allowthe determination of the 1st order image aberrations, namely defocussingand 1st order two-fold astigmatism. The zero-fold component determinedvia the section angle of the difference of the width, that is to say themean value formed via the section angle w, which is therefore directionindependent, provides a dimension figure for the focussing anddefocussing of the electron-optical system. The first order zero-foldimage aberration represents the defocussing.

The two-fold component, determined by the same Fourier analysis, fromthe difference of the widths of the probe profiles, provides, accordingto magnitude and orientation, the value of the aberration of the 1 storder two-fold astigmatism.

From the curvatures of the probe profiles and the differences formedfrom overfocus and underfocus, the individual aberration components ofthe 3rd order image aberrations can also be obtained by an analysis ofthe foldedness via the section angle, carried out, for example, by meansof Fourier analysis. Here, too, particular image aberrations areassigned in dependence on the foldedness, the size of the componentgiving the magnitude and orientation of the image aberration present.For example, the zero-fold component, that is to say the mean value ofthe section angle w, indicates a dimension figure for the 3rd orderspherical aberration. The two-fold component, according to its magnitudeand direction, gives the dimension figure for the 3rd order stellaraberration. Finally, the four-fold component, also according to itsmagnitude and direction, gives the value for the four-fold astigmatism.Thus all 3rd-order electron-optical image aberrations are determined.

Since in real optical systems the 1st and 3rd order image aberrationsare never completely decoupled in width and curvature, a more accuratedetermination of 3rd order aberrations can be carried out using, insteadof the curvature KR or width BR or their respective differences, linearcombinations of the two values according to the aforementioned scheme.The respective associated multiplication factors α and β according tothe formula:α*BR+β*KRmust be determined empirically for each particle-optical system toobtain the best possible results. For the 3rd order sphericalaberrations, the mean value over the section angle w must be formed.

Further scope of applicability of the present invention will becomeapparent from the detailed description given hereinafter. However, itshould be understood that the detailed description and specificexamples, while indicating preferred embodiments of the invention, aregiven by way of illustration only, since various changes andmodifications within the spirit and scope of the invention will becomeapparent to those skilled in the art from this detailed description.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will become more fully understood from thedetailed description given hereinbelow and the accompanying drawingswhich are given by way of illustration only, and thus, are not limitiveof the present invention, and wherein:

FIG. 1 shows a schematic view of a scanning electron microscope;

FIG. 2 shows a flow diagram for determining the probe form;

FIG. 3 shows an analysis of a probe profile; and

FIGS. 4 and 5 show sections through a probe profile.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The exemplary embodiment of the invention shown in FIG. 1 is a scanningelectron microscope, in which electrons are emitted from a source 1,usually an approximately punctiform tungsten tip, and are guided bylenses 2, such as electrical and/or magnetic multipoles, line by lineover the object 3 to be imaged, as indicated by the arrows. Theelectrons radiated back by the object 3, or the secondary electronsemitted from it the object 3, are registered by a suitable detector 4,which registers an image in the form of a brightness or intensitydistribution.

FIG. 2 shows the procedure by which the probe forms 5, 5 a are obtained.To this end, the object 3 is imaged with a focussed, an overfocussed,and an underfocussed particle beam, and subsequently these images 6, 6a, 6 b are subjected to a Fourier transformation. After division 8 ofthe transform 7 a of the overfocussed image by the transform 7 of thefocussed image, and the reverse transformation of the quotient, theinformation about the imaged object 3, which was still contained in theoriginal images 6, 6 a, 6 b, is cancelled out, and, as a result, onlythe form of the probe in overfocus and underfocus 5, 5 a is obtained.The same procedure is carried out for the transform 7 b in underfocus.

Subsequently, as shown in FIG. 3, sections are taken along variousangles through the probe 5, and, the different forms of the sections 9,9 a, as shown in FIGS. 4 and 5, in particular their asymmetry,half-value width or curvature in the center, are used to determine thevarious geometrical-optical aberrations, as described above.

The invention being thus described, it will be obvious that the same maybe varied in many ways. Such variations are not to be regarded as adeparture from the spirit and scope of the invention, and all suchmodifications as would be obvious to one skilled in the art are to beincluded within the scope of the following claims.

1. A method for determining geometrical-optical aberrations up to andincluding 3rd order in particle-optical, probe-forming systems, inparticular scanning electron microscopes that include an essentiallypunctiform source, which emits a particle beam, lenses for influencingthe particle beam, the particle beam having particles that image anobject, and a detector for registering the particles or imaging theobject, the method comprising: imaging the object by the particle beam,which is focussed on the object; recording the image; repeating theimaging and recording steps utilizing an overfocussed and anunderfocused beam, which produce overfocussed and underfocussed images;transforming the overfocussed and underfocussed images in Fourier space;dividing the transformation of the overfocussed image by a transformedfocussed image thereby obtaining a first quotient; and dividing thetransformation of the underfocussed image by the transformed focussedimage, thereby obtaining a second quotient, wherein the first and secondquotients are reverse transformed and thereby brightness profiles of theprobes, are determined, the asymmetry of the profiles with respect to acenter, a width of the profiles, in particular the half-value width,and/or the curvature of the profiles in the center are determined, andwherein differences of the profiles of the probes are used to determinethe image aberrations.
 2. The method according to claim 1, wherein theFourier transformation and/or the reverse transformation is obtained bymathematical and/or optical means, preferably by generating adiffraction pattern.
 3. The method according to claim 1, wherein theparticle beam is influenced with electrical and/or magnetic multipoles.4. The method according to claim 1, wherein the width of the defocusedimage of the source is at least ten times greater than the width of thefocused image of the source or of the source itself.
 5. The methodaccording to claim 1, wherein sections are taken at angular intervals,in particular every 15 degrees, through the probe profiles in overfocusand underfocus, and the brightness profiles, the asymmetry, and thewidth of the probes are determined for each section.
 6. The methodaccording to claim 5, wherein, for determining a image aberration of 2ndorder axial coma, the mean values of the asymmetries of the sectionsthrough the probes in overfocus and underfocus in dependence on sectionangles “w” are formed, and a magnitude and orientation of one-foldcomponents of these mean values are determined, preferably by Fourieranalysis with respect to the section angle “w”.
 7. The method accordingto claim 5, wherein, for determining a image aberration of three-fold2nd order astigmatism, mean values of the asymmetries of the sectionsthrough the probes in overfocus and underfocus in dependence on sectionangle “w” are formed, and a magnitude and orientation of these meanvalues are determined, preferably by Fourier analysis over the sectionangle “w”.
 8. The method according to claim 5, wherein, for determininga defocussing, the difference between the widths of the sections throughthe probes in overfocus and underfocus in dependence on the sectionangle “w” is formed, and a magnitude of a zero-fold component of thesedifferences are determined preferably by Fourier analysis over thesection angle “w”.
 9. The method according to claim 5, wherein, fordetermining a two-fold 1st order astigmatism, the difference between thewidths of the sections through the probes in overfocus and underfocus independence on the section angle “w” is formed, and a magnitude of atwo-fold component of this difference is determined, preferably byFourier analysis over the section angle “w”.
 10. The method according toclaim 5, wherein, for determining a 3rd order spherical aberration, thedifference between the curvature of the sections through the probes inoverfocus and underfocus is formed in dependence on the section angle“w” and a magnitude of a zero-fold component of these differences isdetermined, preferably by Fourier analysis over the section angle “w”.11. The method according to claim 5, wherein, for determining a 3rdorder stellar aberration, the difference between the curvature of thesections through the probes in overfocus and underfocus is formed independence on the section angle “w”, and a magnitude of the two-foldcomponent of the difference is determined, preferably by Fourieranalysis over the section angle w”.
 12. The method according to claim 5,wherein, for determining a four-fold 3rd order astigmatism, thedifference between the curvature of the sections through the probes inoverfocus and underfocus in dependence on the section angles “w” isformed, and a magnitude of the two-fold component of these thedifference is determined, preferably by Fourier analysis over thesection angle “w”.
 13. The method according to claim 10, wherein, fordetermining a 3rd order spherical aberration, instead of the differencein curvature, the difference of a linear combination of curvature andwidth is used in the equation:α*BR+β*KR wherein α and β is determined empirically and represents arespective mean value with respect to the section angle “w”.